Question

Why is the median useful?

Answer 1

Hint: We first explain the concept of median and the differences for discrete data and continuous data. The fixed number of inputs makes the median similar toa average of the numbers.

Complete step by step answer:
The median is used for location measurement as it reduces the importance to extreme values.
For a given data set, if the points are distributed which have skewness or extreme values in the form of outliers then we can’t use the central tendency method of mean. The one skewed point changes the result drastically.
An outlier can affect the mean by being unusually small or unusually large. The mean is non-resistant. The mean will want to move towards the outlier and that’s why we use median more than mean in measures of central tendency.
We take an example: Ten students take a test and get the following scores of $0,88,90,92,94,95,95,96,97,99$.
The mean becomes \[\overline{x}=\dfrac{0+88+90+92+94+95+95+96+97+99}{10}=\dfrac{846}{10}=84.6\].
The sample means becomes 94 if we just remove the data 0.
In this case an unusually low score of one student drags the mean down for the entire dataset.

Note:
Usually the average is very different from the mean or average. The median is more shifted towards the middle of the number of values irrespective of the difference between numbers and their individual values. Half is distributed to the left and the other half is on the right side of the median.